None of the four were willing to change their votes, and the meeting ended without an appointment. If the board does not choose a supervisor by June 19, the decision would be left to Gov. Jerry Brown.

“My feeling would be to leave it to the governor,” said Miley. “Unless I’m given a significant reason to alter my vote from Richard Valle, I’ve got to hold firm to that.”

Whoever is appointed is expected to run for the office in November, and Carson had been concerned about the appearance that supervisors would give the advantage of incumbency to anyone they appointed. Carson wanted to appoint someone who would not run for re-election — former Supervisor Gail Steele — to avoid that situation.

Miley, Chan, Brown and Valle were all part of an endorsement and fundraising machine that helped put Lockyer, who had no elected experience in the county, into office. Lockyer’s husband, state Treasurer Bill Lockyer, fueled her record $1.6 million 2010 campaign.

Valle, the president of a nonprofit recycling company in Union City, said he would trust the governor’s decision.

“The governor is a solid Democrat,” said Valle. “He’s a decision maker. I have faith in his judgment.”

Nonetheless, both Valle and Apodaca criticized the board for failing to make a choice.

“Unfortunately, that’s what happens in politics,” said Valle. “Everybody punts to somebody else … I think that’s one of the real issues around leadership: you’ve got to make a decision.”

Valle served on the Union City council for 12 years and the board of St. Rose Hospital for eight years

Apodaca and Valle each scoffed at suggestions from Chan and Miley that they confer with each other and see if one would concede.

“This is their decision to make,” said Apodaca. “They have to make it. That’s when leadership comes in. They have to make decisions in difficult times.”

Apodaca has been on the Newark City Council since 2005 and was the former District Director for state Sen. Liz Figueroa from 1998 to 2004. Figueroa was the top contender to Nadia Lockyer in the 2010 supervisorial race.

The District 2 vacated by Lockyer runs from Hayward through part of Fremont. It’s the most heavily Latino district in the county, leading to pressure that the seat be filled by a Latino. Chan noted that there had only been six women supervisors in the history of Alameda County, which was established in 1853.

“You have a chance to strike a blow for equal representation for a growing population,” said Elsa Ortiz, president of the AC Transit Board of Directors.